Antiferromagnetically coupled multilayers with perpendicular anisotropy, as [CoPt]/Ru, Co/Ir, Fe/Au, display ferromagnetic stripe phases as the ground states. It is theoretically shown that the antiferromagnetic interlayer exchange causes a relative shift of domains in adjacent layers. This ``exchange shift is responsible for several recently observed effects: an anomalous broadening of domain walls, the formation of so-called ``tiger-tail patterns, and a ``mixed state of antiferromagnetic and ferromagnetic domains in [CoPt]/Ru multilayers. The derived analitical relations between the values of the shift and the strength of antiferromagnetic coupling provide an effective method for a quantitative determination of the interlayer exchange interactions.
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